OCR DC Circuits Module 1 Notes

Module No.1: Introduction to DC Circuits Outline 1. Electricity 2. Nature Electricity 3. Ohm’s Law 4. Law of Resistance 5. Circuits Elements 6. Voltage and Current Sources 7. Ideal and Practical Voltage/Current Sources Electricity The invisible energy which constitutes fl...

Module No.1: Introduction to DC Circuits Outline 1. Electricity 2. Nature Electricity 3. Ohm’s Law 4. Law of Resistance 5. Circuits Elements 6. Voltage and Current Sources 7. Ideal and Practical Voltage/Current Sources Electricity The invisible energy which constitutes flow of electrons in a closed circuit to do work is called electricity. Electricity plays an important role in our day to day life. Electricity is used for: 1. Lighting ( lamps) 2. Heating( heaters) 3. Cooling 4. Entertainment ( T.V. and radio) 5. Transportation 6. Calculations( Calculators) Now- a- days all the activities are dependent upon electricity. Nature of Electricity Every matter is electrical in nature since it contains charged particles like electrons and protons. Therefore, 1. Ordinarily, a body is neutral as it contains same number of protons and electrons. 2. If some of electrons are removed from the body, there is a deficit of electrons and the body attains a positive charge. 3. If some of electrons are supplied to the body, there occurs excess of electrons and the body attains a negative charge. Nature of Electricity A body is said to be positively charged or negatively charged if it has deficit or excess of electrons from its normal due share respectively. Unit of Charge: The practical unit of charge is coulomb. One Coulomb= charge on 6.28 x 1018 electrons. Electricity Free Electrons: The valence electrons which are loosely attached to the nucleus of an atom and free to move when external energy is applied are called free electrons. Electrical Potential: The capacity of charged body to do work is called electrical potential. Unit of electrical potential: Volts or Joules per Coulomb (Joules/Coulomb). NOTE: A body is said to have an electric potential of 1 Volt if 1 Joule of work is done to charge the body to 1 coulomb. Electricity Potential Difference The difference in electrical potential of the two charged bodies is called potential difference. Unit of potential difference is Volts. Electric Current In metallic wire, a large number of electrons are available which move from one atom to other at random. When an electrical potential is applied across a metallic wire, the loosely attached free electron start moving towards positive terminal of the cell. Figure 1-1: (a) Electron flow in metallic wire (b) Comparison between direction of conventional and electron flow (a) (b) Electricity Thus, continuous flow of electrons in an electric circuit is called electric current. Current is rate of flow of electrons, i.e. charge flowing per second. 𝑄 𝐼= 𝑡 where: I = current Q = charge t = time The unit of current is Ampere (A). Electricity Electromotive force(EMF) and Potential Difference: Electromotive force(EMF) EMF is the force that causes an electric current to flow in an electric circuit. In fact, it is not a force but rather an energy. The electromotive force is the amount of energy supplied by the source to each coulomb of charge. Potential Difference The potential difference is the amount of energy used by the one coulomb of charge in moving from one point to the other. In Figure 1-2, battery has emf of 12V and the potential difference between A and B is 7V. Figure 1-2: Potential difference between point A and point B Ohm’s Law Ohms laws state that the current through any two points of the conductor is directly proportional to the potential difference applied across the conductor, provided physical conditions i.e. temperature, etc. do not change. It is measured in (Ω) ohm. Mathematically it is expressed as: This constant is also called the resistance (R) of the conductor (or circuit). 𝑉 𝑅= 𝐼 Ohm’s Law In a circuit, when current flows through a resistor, the potential difference across the resistor is known as voltage drops across it, i.e., V = IR. Limitations of Ohm’s Law Ohm’s law is not applicable in unilateral networks. Unilateral networks allow the current to flow in one direction. Such types of network consist of elements like a diode, transistor, etc. It is not applicable for the non-linear network (network containing non- linear elements such as electric arc etc). In the nonlinear network, the parameter of the network is varied with the voltage and current. Their parameter likes resistance, inductance, capacitance and frequency, etc., not remain constant with the times. So Ohms law is not applicable to the nonlinear network. Ohm’s law is used for finding the resistance of the circuit and also for knowing the voltage and current of the circuit. Ohm’s Law Resistance The opposition offered to flow of current is called resistance. It is represented by R. The unit of resistance is ohms (Ω). The resistance of a given length of wire is given in Figure 1-3. (a) (b) Figure 1-3: (a) Resistance of a given length of wire and (b) its equivalent circuit symbol Law of Resistance The resistance of a wire depends upon: 1. It is directly proportional to its length RαL 2. It is inversely proportional to its area of cross-section. 1 𝑅α 𝐴 3. It depends upon the nature of material of which the wire is made. 4. It also depends upon the temperature of the wire. Combining the two equations given above yields: 𝐿 𝑅= 𝐴 Law of Resistance The proportionality constant  is called the specific resistance or resistivity of the conductor and its value depends on the material of which conductor is made. The inverse of the resistance is called the conductance (G) and inverse of resistivity is called specific conductance or conductivity, designated by symbol . Thus, conductivity is  = 1/ and its units is Siemens per meter. 𝐴 𝐺= 𝐿 EXAMPLE#1: Find the cross-sectional area, in2 , of a piece of copper wire, 40 m in length and having a resistance of 0.25 Ω. Assume resistivity of copper is 0.02×10−6 Ω-m. EXAMPLE#2: Calculate the resistivity of a material with a resistance of 2 and a cross-sectional area and length of 25 cm2 and 15 cm, respectively. EXAMPLE#3: A wire of length 1 m has a resistance of 2 . Obtain the resistance if specific resistance is double, the diameter is doubled, and the length is made three times the first. Electric Circuit The close path for flow of electric current is called electric circuit. The electric circuit is an arrangement of electrical energy sources and various circuit elements such as R, L and C that can be connected in series, parallel, or series-parallel combinations. Circuit Elements: The circuit elements can be categorized as: 1. Active and passive elements 2. Unilateral and bilateral elements 3. Linear and non-linear elements 4. Lumped and distributed elements Circuit Elements 1. Active and Passive elements Active elements are those who supply energy or power in the form of a voltage or current to the circuit or network. Examples of the active components are batteries or generators etc. Passive elements are those who receive energy in the form of voltage or current. Examples of the passive components are resistor, capacitor and inductor. 2. Unilateral and Bilateral elements Unilateral elements are elements which conduct the current in one direction only, such as diodes, transistors, vacuum tubes, rectifiers, etc. Bilateral elements are elements which conduct the current in both the directions such as resistors. Circuit Elements 3. Linear and Non-linear elements Linear Elements are elements which follow the linear relation between current and voltage, e.g. resistors. Non-Linear Elements are elements which don‟t follow the linear relation between current and voltage. e.g. Diode and transistors 4. Lumped and distributed elements Lumped elements are elements in which action takes place simultaneously such as resistor, capacitor and inductor. These elements are smaller in size. Distributed elements are elements in which for a given cause is not occurring simultaneously at the same instant but it is distributed such as transmission lines. Voltage and Current Sources To deliver electrical energy to the electrical circuits, a source is required, and a load is connected to source as shown in figure 1-4. The source may be DC source or AC source. (a) (b) Figure 1-4: (a) DC Source connected to load (b) AC Source connected to load Voltage and Current Sources 1. D.C. source Any source that produces direct voltage continuously and has ability to deliver direct current is called DC source such as batteries and generators. 2. A.C. source Any source that produces alternating voltage continuously and has ability to deliver the alternating current is called AC source such as alternators, oscillators or signal generators. Independent and dependent sources There are two types of sources- voltage source and current source. Sources can be either independent or dependent upon some other quantities. 1. Independent voltage/current source (a) (b) The voltage ( AC or DC) does not dependent on other voltages or current in the circuit. Symbol for independent voltage and current source is shown in figure 1-5. Figure 1-5: (a) DC voltage source (b) AC voltage source Voltage and Current Sources NOTE: Examples of independent voltage source are batteries and generators. Examples of independent current source are semiconductor devices such as Diode and transistors. 2. Dependent voltage/current source The voltage does dependent on another voltage or current in the circuit. Symbol for dependent voltage and current source is shown in figure 1-6. (a) (b) Figure 1-6: (a) Independent or controlled voltage source (b) Independent or controlled current source Ideal and Practical Voltage/Current Sources Ideal Voltage Source Refers to an imaginary voltage source, which can provide a constant voltage to load ranging from zero to infinity. Such voltage source is having zero internal resistance (Rs) and is called Ideal Voltage Source. Practically it is not possible to build a voltage source with no internal resistance and constant voltage for that long range of the load. (a) (b) Figure 1-7: (a) Ideal voltage source (b) Practical voltage source Ideal and Practical Voltage/Current Sources Practical Voltage Source Practical voltage sources always have some resistance value in series with an ideal voltage source and because of that series resistance, voltage drops when current passes through it. So, Practical Voltage Source has internal resistance and slightly variable voltage as shown in figure 1-7b. Ideal Current Source: An ideal current source has infinite resistance. Infinite Resistance is equivalent to zero conductance. Practical current source: Practical current source is equivalent to the ideal current source in parallel with high resistance or low conductance. Practical Current Source Practical current source is equivalent to the ideal current source in parallel with high resistance or low conductance as shown in figure 1-8b. Ideal and Practical Current Sources (a) (b) Figure 1-8: (a) Ideal current source (b) Practical current source References: https://circuitglobe.com/voltage-source-and-current-source.html https://www.cecmohali.org/public/documents/applied/material/notes/Module%201(DC%20 circuits).pdf